Luis is 2 times as old as Brandon. 42 years ago, Luis was 9 times as old as Brandon. How old is Brandon now?
Answer: We can use the given information to write down two equations that describe the ages of Luis and Brandon. Let Luis's current age be $l$ and Brandon's current age be $b$ The information in the first sentence can be expressed in the following equation: $l = 2b$ 42 years ago, Luis was $l - 42$ years old, and Brandon was $b - 42$ years old. The information in the second sentence can be expressed in the following equation: $l - 42 = 9(b - 42)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = 2b$ . Substituting this into our second equation, we get: $2b$ $-$ $42 = 9(b - 42)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $2 b - 42 = 9 b - 378$ Solving for $b$ , we get: $7 b = 336.$ $b = 48$.